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autonomous convergence theorem
In mathematics, an autonomous convergence theorem is one of a family of related theorems which specify conditions guaranteeing global asymptotic stability of a continuous autonomous dynamical system.
==History==
The Markus–Yamabe conjecture was formulated as an attempt to give conditions for global stability of continuous dynamical systems in two dimensions. However, the Markus–Yamabe conjecture does not hold for dimensions higher than two, a problem which autonomous convergence theorems attempt to address. The first autonomous convergence theorem was constructed by Russell Smith.〔Russell A. Smith, "Some applications of Hausdorff dimension inequalities for ordinary differential equations", ''Proceedings of the Royal Society of Edinburgh Section A'', 104A:235–259, 1986〕 This theorem was later refined by Michael Li and James Muldowney.〔Michael Y. Li and James S. Muldowney, "On R. A. Smith's autonomous convergence theorem", ''Rocky Mountain Journal of Mathematics'', 25(1):365–379, 1995〕
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